Tension of Rope: Cosmonaut & Spaceship Orbit in Planetary Gravity

In summary, the problem involves a cosmonaut of mass 100 kg outside of a spaceship of mass 5000 kg, connected by a rope of length 64 m. The cosmonaut and spaceship are in orbit around a planet with a mass of 6*10^24 kg and a radius of 6400 km. The task is to calculate the tension in the rope, taking into account the negligible distance between the orbit and the planet's surface. Using the universal gravitation law, the gravitational attraction between the cosmonaut and spaceship is found to be 8.14208984375×10^-9 N. However, the tension in the rope must also be considered in order to determine the final answer.
  • #1
Jorgen1224
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Homework Statement


What is the tension of this rope?
Cosmonaut m=100kg is outside of spaceship M=5 tons on rope with length 64m. Cosmonaut along with his spaceship moves in orbit at a neglible distance.

m=100kg
M=5000kg
L=64m
Planet's mass 6*10^24
Planet's radius 6400km

Homework Equations


4ea196e90833059c9d91cd86bea05e3ec8b75d24

Kepler's 3rd law(maybe?)

The Attempt at a Solution



It's from physics olympics, so i bet that it requires one complex idea.
What comes out of universal gravitation law is 8.14208984375×10^-9 N and I'm not sure what to do afterwards.
 
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  • #2
Is the statement of the problem exactly as it was given in the physics Olympics? I am not sure what "negligible distance" means. Negligible relative to the radius of the planet or negligible relative to 64 m?
 
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  • #3
kuruman said:
Is the statement of the problem exactly as it was given in the physics Olympics? I am not sure what "negligible distance" means. Negligible relative to the radius of the planet or negligible relative to 64 m?
My guess is that the "negligible" refers to the orbital altitude above the planet's surface. The input data is good to one significant figure. So the use of reasonable approximations is apparently encouraged.

Perhaps the first order of business is to pick a frame of reference to use. An inertial frame nailed to the planet's center? A rotating frame nailed to the planet as a whole? Then the free body diagrams.
 
  • #4
jbriggs444 said:
My guess is that the "negligible" refers to the orbital altitude above the planet's surface.
That would also be my guess, because otherwise the answer is trivial. However, I still would like to see the statement of the problem if it is different from the posted one.
 
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  • #5
Jorgen1224 said:
Cosmonaut m=100kg is outside of spaceship M=5 tons
Jorgen1224 said:
M=5000kg
I'm still trying to parse this part...
 
  • #6
Jorgen1224 said:
What comes out of universal gravitation law is 8.14208984375×10^-9 N
That is the gravitational attraction between the cosmonaut and the spacecraft based on their respective masses and separation. That could be important if we had a pole holding them apart. But in the case at hand we have a rope holding them together. What other force tends to separate the two?

[Note that it is easier to provide help when more of the work is shown and one does not have to reverse-engineer the result to figure out what went wrong]
 

1. What is the tension of a rope in a cosmonaut and spaceship orbit in planetary gravity?

The tension of a rope in this scenario is the force that it exerts on the cosmonaut and spaceship as they orbit around a planet. This tension is what keeps them in orbit and prevents them from drifting away.

2. How is the tension of the rope calculated in this situation?

The tension of the rope is calculated by using the formula T = m(v^2/r), where T is the tension, m is the mass of the cosmonaut and spaceship, v is the velocity of their orbit, and r is the distance between them and the center of the planet. This formula takes into account the gravitational force exerted by the planet on the cosmonaut and spaceship, as well as their centrifugal force due to their orbit.

3. Does the tension of the rope change as the cosmonaut and spaceship orbit around the planet?

Yes, the tension of the rope changes as the cosmonaut and spaceship orbit around the planet. As they move closer to the planet, the tension increases due to the stronger gravitational force. As they move further away, the tension decreases.

4. Can the tension of the rope be adjusted during the orbit?

Yes, the tension of the rope can be adjusted during the orbit. This can be done by changing the velocity of the cosmonaut and spaceship, either by using thrusters or by adjusting their trajectory. By changing the velocity, the centrifugal force and therefore the tension of the rope will also change.

5. What happens to the tension of the rope if the cosmonaut and spaceship enter a different planet's gravitational field?

If the cosmonaut and spaceship enter a different planet's gravitational field, the tension of the rope will change accordingly. This is because the mass and velocity of the cosmonaut and spaceship will be different, as well as the distance between them and the center of the new planet. Therefore, the tension of the rope will need to be recalculated using the new variables.

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